The concept of randomness is
historically a recent development (in the 1700's). Even more
recently in the 20th century, randomness and probability (involving
subatomic particles) have been embraced by quantum physics.

Einstein: "God does NOT
play dice with the Universe!"

Some people reject the notion of randomness on
religious or philosophical grounds. They do not accept
the idea that events in our world can occur randomly.
Whether or not you share this belief, you can still have
fun trying to act randomly in this exercise.

You might want to consider this controversial idea: If you
believe in the notion of "free will," then you must
believe that human behavior is ultimately random! If you could
know ahead of time what course of action a person would choose,
then his/her choice is not completely "free." If the
choice is determined by past history, personality, or current
forces, then how could the choice result from "free will?"
Freedom implies some capriciousness or haphazardness. Because the
behavioral psychologist B.F. Skinner believed
that our behavior was totally determinedby our past history,
genetic endowments, and current forces, he denied the possibility
of free will, or even freedom.

Dictionary definitions emphasize the notion of "apparent
absence of cause, planning, or design," "lack
of method or system," or "accidental, haphazard."
Statistical definitions, which we will use in this
exercise, involve the inability to predict outcomes or to
find any pattern in a series of outcomes. To level 2 and level 3 for more
on definition problems

Some people use the word to mean that something can't be
explained with current theory (In which case this is just
admitting ignorance or that the theories are lousy.). Or
they might mean that the causes can never be fully
specified. The implication here is that all events are
deterministically caused, but our knowledge of the causes
will always be incomplete, making them act as if they
were randomly determined. The distinction is between
an event being indeterminate (truly caused by chance)
versus being indeterminable (governed by variables we
cannot measure).

Why you should care about randomness--even
if you don't gamble

You are curious about what causes things to
happen. The only way scientists can prove
causation is to rule out the possibility that a
potential cause and an effect are associated by
chance or randomness. Before we accept the claim
that drug X cures disease Z, we have to determine
that the improvement is better than what we would
expect by chance alone.

Every-day transactions use random numbers. When
you use an automatic teller machine, your
requests and account information are encrypted
with a "key" which is usually randomly
generated. If this process is flawed and the
criminals know how it is flawed, they can clear
out your account!

Many important systems (including
the military's security of nuclear weapons)
depend on randomness or encryption which
supposedly cannot be broken by hackers. Recently,
the media reported that the most commonly used
"64-bit DES" encryption algorithm was
broken by scientists who used only $250,000 worth
of computers running for only 57 hours. Before we
can feel safe from criminals or terrorists, we'll
need to develop a more elaborate system of
encryption!!

One definition of randomness implies that the
number of heads equals the number of tails.
With an unbiased coin, there should, on
average, be 50 heads in 100 flips. According
to statistical theory, the number of heads
will equal the number of tails only in an
infinite series of flips. Since 100 outcomes
is far less than infinite, the number of
heads will not equal exactly 50 and will vary
around that value with a normal
distribution (level 2 + 3 stats digression). About
two-thirds of the time, random processes will
yield between 45-55 heads. Rarely (less than
5% of the time), will the number of heads
fall outside the 41-59 range.

The concept of runs: number and length.
A run is a repeated outcome. A run is defined
as a sequence of repeating heads or tails. A
new run occurs when a new symbol appears. For
example, if 3 flips of a coin produce "HTT,"
there are two runs: one of length 1--the
first H, and one of length 2 --the second and
third "T." Many people mistakenly
think that a random coin toss would produce
alternating sequences of HTHTHTHT... Although
a randomly flipped coin might produce this
once in a while, it is highly unlikely.
Failures in randomness could produce too
many runs (more than 60) or too few (less
than 40) in a given sequence, and their
length could be either too short (less than 4)
or too long (more than 10).level
2+3 stats digression.

Serial dependencies or autocorrelations:
One randomness requirement is that there are
few patterns and they don't repeat very often.
Thus, the fact that an H has occurred on a
flip should not influence whether an H
happens on the next flip. The alternating
heads/tails pattern above violates this
requirement because every time an H occurs,
it is followed by a T, creating a pattern.
This can only occur if the coin could "remember"
what had happened on the previous flip.

In
random sequences, the probability of an H
happening on the next flip should be
unchanged by what happened in the previous
flip, two flips before, etc. If the
probability of a head following a head is
different from the probability of a head
following a tail by more than .20, then there
is a serial dependency problem which suggests
a lack of randomness.level 2 + 3
elaboration

If you are now ready to see how random your
sequence was, click the "analyze" button.

How does your random sequence stack up to the one
theoretically predicted to be random? If you can't
remember what the values of the 4 statistical tests
should be, click here to go
to a summary table of results where the expected
values are displayed along with the results for your
sequence.

Most people generate a sequences which have too
many runs, runs which are too short, and too many/few
heads. By the way, please
wait until later on in this exercise to try entering
another imaginary coin flip series.

Why might someone have too many/few heads?

People won't bother to keep track of the
number of heads as they respond. But this
begs the question, why would they prefer one
response ( H) over another (T)?

People may be superstitious, associating
heads or tails with good things.

People may unconsciously prefer one letter
over the other and type it more often. People
named "Tom" may type "T"
more often than people named "Harry."

The way the keyboard is set up, most people
will type "H" with their right-hand
finger and "T" with their left-hand
finger. Maybe left-handed people will type
"T" more often and right-handed
people "H" because it is a more
dominant response.

If you were like most people, your random sequence
wasn't so random, especially in terms of the number
of runs and their length. There are a number of
reasons why.

The gambler's fallacy
occurs because people assume that chance or
randomness is self-correcting. So, if "red"
has won 5 times in a row at the roulette wheel,
people think that "black" is due. Assuming
the roulette wheel is fair, the probability of black
is unchanged. This fallacy may be due to people's
misunderstandings of conditional probabilities. digression: a probability
teaser (levels 1-3).

A related fallacy is the hot hand fallacy.
People think that repeating outcomes are caused by (unseen)
forces and don't recognize them as being the result
of chance. For example Gilovich,
Vallone, and Tversky (1985) have shown that
basketball players may think they are in a shooting
streak even though their pattern of hits and misses
doesn't deviate from what you would expect to happen
by chance. Gilovich finds that people see streaks
when the events do not deviate from a random process.
People think that events repeat less often than they
actually do. This causes them to view random events
as being significant or meaningful when they really
aren't.

Some processes, like coin
flipping, are not truly random and are called
"pseudo-random." If you knew which
side of the coin was facing up and exactly
how much force was applied to the flip, you
would know how the flip would turn out.
Diaconis, a magician/mathematician, has
taught himself how to apply the right amount
of force so he can flip silver dollars in any
pattern he wishes. He uses this ability in
his "psychic" demonstrations! (He
can't consistently flip a coin with less mass
than a silver dollar).

Take out a coin and flip it 100
times, recording the outcomes in the text box below.
If you want the computer to use a random number
generator to produce the sequence of t's and h's,
click on the "have computer generate"
button.

Research has shown that humans are
not capable of responding randomly when told to do so.
However, Heuringer
(1986) has shown that
people can be trained to respond randomly-- if they
are given trial by trial feedback (about whether
their response is random) much like what this
exercise does. But it took 30 -40 repetitions of this
exercise to "condition" them to respond
with random patterns [and you thought flipping a coin
100 times was boring]!